Systems and methods for implementing tailored metallic glass-based strain wave gears and strain wave gear components

ABSTRACT

Systems and methods in accordance with embodiments of the invention implement tailored metallic glass-based strain wave gears and strain wave gear components. In one embodiment, a method of fabricating a flexspline of a strain wave gear includes: forming a MG-based composition into a flexspline using one of a thermoplastic forming technique and a casting technique; where the forming of the MG-based composition results in a formed MG-based material; where the formed flexspline is characterized by: a minimum thickness of greater than approximately 1 mm and a major diameter of less than approximately 4 inches.

CROSS-REFERENCE TO RELATED APPLICATIONS

The current application is a continuation of U.S. application Ser. No.16/214,848, filed Dec. 10, 2018, which application is a divisional ofU.S. application Ser. No. 15/062,902, filed Mar. 7, 2016, which claimspriority to U.S. Provisional Application No. 62/128,827, filed Mar. 5,2015, the disclosures of which are incorporated herein by reference intheir entireties.

STATEMENT OF FEDERAL FUNDING

The invention described herein was made in the performance of work undera NASA contract NNN12AA01C, and is subject to the provisions of PublicLaw 96-517 (35 USC 202) in which the Contractor has elected to retaintitle.

FIELD OF THE INVENTION

The present invention generally relates to metallic glass-based strainwave gears and strain wave gear components.

BACKGROUND

Strain wave gears, also known as harmonic drives, are unique gearingsystems that can provide high reduction ratios, high torque-to-weightand torque-to-volume ratios, near-zero backlash (which can mitigate thepotential wearing of the components), and a host of other benefits.Typically, strain wave gears include an elliptical wave generator thatis fitted within a flexspline such that the flexspline conforms to theelliptical shape of the wave generator; this arrangement also typicallyincludes a set of ball bearings that allow the flexspline to rotateabout the central axis of the elliptical shape relative to the wavegenerator. The flexspline is generally disposed within a ring-shapedcircular spline, where the flexspline includes a set of gear teeth alongits outer, elliptically shaped, perimeter that engage with gear teethdisposed along the inner circumference of the rim-shaped circularspline. Typically, the flexspline has fewer teeth than the circularspline. Notably, the flexspline is made of a flexible material such thatwhen gear teeth of the flexspline and circular spline are engaged, thewave generator can rotate relative to the circular spline in a firstdirection, and thereby cause the deformation and associated rotation ofthe flexspline in a second opposite direction. Normally, an input torqueis provided to the wave generator, and the flexspline generates aresulting output torque. Typically, the rate of rotation of the wavegenerator is much greater than the rate of rotation of the flexspline.Thus, strain wave gears can achieve high reduction ratios relative togearing systems and can do so in a smaller form factor.

Note that in some alternative arrangements, the flexspline is heldfixed, and the circular spline is used to provide an output torque.

As can be inferred, the operation of a strain wave gear is particularlynuanced and relies on a very precisely engineered gearing system. Forexample, the geometries of the constituent parts of strain wave gearsmust be fabricated with extreme accuracy in order to provide the desiredoperation. Moreover, the strain wave gear components must be fabricatedfrom materials that can provide for the desired functionality. Inparticular, the flexspline must be flexible enough to withstandhigh-frequency periodic deformation, while at the same time being strongenough to accommodate the loads that the strain wave gear is anticipatedto be subjected to.

Because of these constraints, heritage strain wave gears have largelybeen fabricated from steel, as steel has been demonstrated to possessthe requisite materials properties, and steel can be machined into thedesired geometries. However, the machining of steel into the constituentcomponents can be fairly expensive. For example, in many instances,steel-based strain wave gears can cost on the order of $1,000 to $2,000largely because of the expensive manufacturing processes.

In some instances, harmonic drives are fabricated from thermoplasticmaterials. Thermoplastic materials (e.g. polymers) can be cast (e.g. viainjection molding processes) into the shapes of the constituentcomponents, and thereby circumvent the expensive machining processesthat are typically implemented in manufacturing steel-based strain wavegears. However, strain wave gears fabricated from thermoplastics may notbe as strong as strain wave gears fabricated from steel.

SUMMARY OF THE INVENTION

Systems and methods in accordance with embodiments of the inventionimplement tailored metallic glass-based strain wave gears and strainwave gear components. In one embodiment, a method of fabricating aflexspline of a strain wave gear includes: forming a MG-basedcomposition into a flexspline using one of a thermoplastic formingtechnique and a casting technique; where the forming of the MG-basedcomposition results in a formed MG-based material; where the formedflexspline is characterized by: a minimum thickness of greater thanapproximately 1 mm and a major diameter of less than approximately 4inches.

In another embodiment, the MG-based composition is formed into aflexspline using a casting technique.

In yet another embodiment, the MG-based composition is formed into aflexspline by casting it around a solid body.

In still another embodiment, the formed MG-based material has anentirely amorphous structure.

In still yet another embodiment, the formed MG-based material is ametallic glass matrix composite.

In a further embodiment, the formed MG-based material is furthercharacterized by the inclusion of gear teeth.

In a yet further embodiment, the gear teeth are S-shaped.

In a still further embodiment, the MG-based composition is aTitanium-based MG-based composition.

In a still yet further embodiment, the method further includes selectinga MG-based composition for implementation based on desired flexsplineperformance.

In another embodiment, the selected MG-based composition includesconstituent alloying elements, the presence of which causes the formedMG-based material to possess at least certain of the desired materialsproperties.

In yet another embodiment, the selected MG-based composition includes atleast one of one of V, Nb, Ta, Mo, and Sn, when it is desired that theMG-based material to be formed be relatively more flexible.

In still another embodiment, the formation of the flexspline is a netshape process.

In still yet another embodiment, the formed flexspline is characterizedby a maximum thickness of less than approximately 3 mm.

In a further embodiment, the MG-based composition is formed using athermoplastic forming technique.

In a yet further embodiment, the thermoplastic forming technique is oneof: a capacitive discharge forming technique; a frictional heatingtechnique; and a blow molding technique.

In a still further embodiment, the forming of the MG-based compositionincludes: heating a first region of the MG-based composition to atemperature greater than the glass transition temperature of theMG-based composition; where at least some portion of the MG-basedcomposition, that is continuous through the thickness of the MG-basedcomposition, is not heated above its respective glass transitiontemperature when the first region is heated to a temperature greaterthan the glass transition temperature; and deforming the MG-basedmaterial within the first region while the temperature of the MG-basedmaterial within the first region is greater than its respective glasstransition temperature.

In a still yet further embodiment, the formed MG-based material has anentirely amorphous structure.

In another embodiment, the formed MG-based material is a metallic glassmatrix composite.

In yet another embodiment, the MG-based composition is a Titanium-basedMG-based composition.

In still another embodiment, the forming of MG-based compositionincludes both a thermoplastic forming technique and a casting technique.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a strain wave gear that can be fabricated from aMG-based material in accordance with certain embodiments of theinvention.

FIGS. 2A-2D illustrate the operation of a strain wave gear in accordancewith certain embodiments of the invention.

FIGS. 3A-3B illustrate the life expectance of strain wave gearsgenerally.

FIGS. 4A-4B illustrate the fatigue properties of MG-based materials thatcan be implemented within strain wave gear components in accordance withcertain embodiments of the invention.

FIG. 5 illustrates the wear-resistance properties of titanium MG-basedmaterials that can be implemented within strain wave gear components inaccordance with certain embodiments of the invention.

FIG. 6 illustrates a method of forming a MG-based strain wave gearcomponent in accordance with certain embodiments of the invention.

FIGS. 7A-7D illustrate the formation of a gear using casting techniquesin accordance with certain embodiments of the invention.

FIGS. 8A-8D illustrate the fabrication of a strain wave gear componentusing a casting technique in accordance with certain embodiments of theinvention.

FIGS. 9A-9C illustrate the fabrication of a strain wave gear componentusing a MG-based material in the form of a sheet in conjunction with athermoplastic forming technique in accordance with certain embodimentsof the invention.

FIGS. 10A-10C illustrate the fabrication of a strain wave gear componentusing a spin forming technique in accordance with certain embodiments ofthe invention.

FIGS. 11A-11C illustrate the fabrication of a strain wave gear componentusing a blow molding technique in accordance with certain embodiments ofthe invention.

FIGS. 12A-12B illustrate using centrifugal casting to form a strain wavegear component in accordance with certain embodiments of the invention.

FIGS. 13A-13C illustrate forming a strain wave gear component bythermoplastically forming MG-based material in the form of powder inaccordance with certain embodiments of the invention.

FIG. 14 illustrates using twin roll forming to implement gear teeth ontoa MG-based strain wave gear component in accordance with certainembodiments of the invention.

FIGS. 15A-15F illustrate the formation of a flexspline according to theprocess outlined in FIG. 6 in accordance with certain embodiments of theinvention.

FIG. 16 illustrate that casting processes should be well-controlled infabricating a strain wave gear component in accordance with certainembodiments of the invention.

FIG. 17 illustrates that strain wave gear components can be fabricatedon any suitable scale in accordance with certain embodiments of theinvention.

FIGS. 18A-18B illustrate the fabrication of a circular spline inaccordance with certain embodiments of the invention.

FIG. 19 illustrates the cost benefits of casting or thermoplasticallyforming strain wave gear components from MG-based materials inaccordance with certain embodiments of the invention.

FIG. 20 illustrates a steel-based flexspline.

FIG. 21 illustrates forming a relatively smaller strain wave gearflexspline in accordance with certain embodiments of the invention.

FIGS. 22A-22C illustrate flexsplines having relatively thicker walls inaccordance with certain embodiments of the invention.

FIG. 23 illustrates a conventional steel-based flexspline relative to athicker MG-based flexspline in accordance with an embodiment of theinvention.

FIGS. 24A-24B illustrate S-shaped gear teeth that can be implemented inaccordance with certain embodiments of the invention.

DETAILED DESCRIPTION

Turning now to the drawings, systems and methods for implementingtailored metallic glass-based strain wave gears and strain wave gearcomponents are illustrated.

Metallic glasses, also known as amorphous alloys (or alternativelyamorphous metals), are characterized by their disordered atomic-scalestructure in spite of their metallic constituent elements—i.e., whereasconventional metallic materials typically possess a highly orderedatomic structure, metallic glass materials are characterized by theirdisordered atomic structure. Notably, metallic glasses typically possessa number of useful material properties that can allow them to beimplemented as highly effective engineering materials. For example,metallic glasses are generally much harder than conventional metals, andare generally tougher than ceramic materials. They are also relativelycorrosion resistant, and, unlike conventional glass, they can have goodelectrical conductivity. Importantly, the manufacture of metallic glassmaterials lends itself to relatively easy processing. In particular, themanufacture of a metallic glass can be compatible with an injectionmolding process, or any similar casting process.

Nonetheless, the manufacture of metallic glasses presents challengesthat limit their viability as engineering materials. In particular,metallic glasses are typically formed by raising a metallic alloy aboveits melting temperature, and rapidly cooling the melt to solidify it ina way such that its crystallization is avoided, thereby forming themetallic glass. The first metallic glasses required extraordinary cooingrates, e.g., on the order of 10⁶ K/s, and were thereby limited in thethickness with which they could be formed. Indeed, because of thislimitation in thickness, metallic glasses were initially limited toapplications that involved coatings. Since then, however, particularalloy compositions that are more resistant to crystallization have beendeveloped, which can thereby form metallic glasses at much lower coolingrates, and can therefore be made to be much thicker (e.g., greater than1 mm). These thicker metallic glasses are known as ‘bulk metallicglasses’ (“BMGs”.)

In addition to the development of BMGs, ‘bulk metallic glass matrixcomposites’ (BMGMCs) have also been developed. BMGMCs are characterizedin that they possess the amorphous structure of BMGs, but they alsoinclude crystalline phases of material within the matrix of theamorphous structure. For example the crystalline phases can exist in theform of dendrites. The crystalline phases can allow the material to haveenhanced ductility, compared to where the material is entirelyconstituted of the amorphous structure. BMGs and BMGMCs can be referredto collectively as BMG-based materials. Similarly, metallic glasses,metallic glasses that include crystalline phase inclusions, BMGs, andBMGMCs can be referred to collectively as metallic glass-based materialsor MG-based materials.

Even with these developments, the current state of the art has yet tofully appreciate the advantageous materials properties of MG-basedmaterials. As a consequence, MG-based materials have seen limited use inengineering applications. For example, various publications haveconcluded, and it is largely established, that the viability of MG-basedmaterials is mostly limited to microscale structures. (See e.g., G.Kumar et al., Adv. Mater. 2011, 23, 461-476, and M. Ashby et al.,Scripta Materialia 54 (2006) 321-326, the disclosures of which arehereby incorporated by reference.) This is in part because the materialproperties, including the fracture mechanics, of MG-based materials arecorrelated with the specimen size. For example, it has been observedthat the ductility of a MG material is inversely correlated with itsthickness. (See e.g., Conner, Journal of Applied Physics, Volume 94,Number 2, Jul. 15, 2003, pgs. 904-911, the disclosure of which is herebyincorporated by reference.) Essentially, as component dimensions becomegreater, they become more and more prone to brittle failure. Thus, forthese reasons and others, those skilled in the art have generallycounseled that although MG-based materials may make for excellentmaterials for microscale structures, e.g. MEMS devices, they generallyshould not be used for macroscale components. (See e.g., G. Kumar etal., Adv. Mater. 2011, 23, 461-476.) Indeed, G. Kumar et al. haverelated brittle failure to the plastic zone size, and have generalizedthat a specimen thickness of approximately 10 times the plastic zoneradius can exhibit 5% bending plasticity. (Id.) Thus, G. Kumar et al.conclude that a 1 mm thick specimen of Vitreloy can exhibit 5% bendplasticity. (Id.)

While the conventional understanding has suggested limited applicationsfor MG-based materials, it has also touted the wear-resistant aspects ofMG-based materials. (see e.g., Wu, Trans. Nonferrous Met. Soc. China 22(2012), 585-589; Wu, Intermetallics 25 (2012) 115-125; Kong, Tribal Lett(2009) 35:151-158; Zenebe, Tribol Lett (2012) 47:131-138; Chen, J.Mater. Res., Vol. 26, No. 20, Oct. 28, 2011; Liu, Tribol Lett (2012)46:131-138; the disclosures of which are hereby incorporated byreference.) To be clear, “wear” conventionally refers to thedisplacement of the surface of a material as a direct result of itsmechanical interaction with another material. It is generally understoodthat a material's resistance to wear generally increases with itshardness, i.e. the harder a material is, the less susceptible it is towear. (See e.g., I. L. Singer, Wear, Volume 195, Issues 1-2, July 1996,Pages 7-20.) Based on these understandings, it has been suggested thatthe predicted wear-resistance characteristics of MGs may make themexcellent candidates for materials from which to fabricate miniaturegears, given that gears are subject to extensive mechanical interactionand are thereby subject to wear. (See e.g., Chen, J. Mater. Res., Vol.26, No. 20, Oct. 28, 2011; Huang, Intermetallics 19 (2011) 1385-1389;Liu, Tribol Lett (2009) 33:205-210; Zhang, Materials Science andEngineering A, 475 (2008) 124-127; Ishida, Materials Science andEngineering A, 449-451 (2007) 149-154; the disclosures of which arehereby incorporated by reference.) Thus, in accordance with theabove-described insights, gears on a microscale have been fabricated(See e.g., Ishida, Materials Science and Engineering A, 449-451 (2007)149-154, the disclosure of which is hereby incorporated by reference.)

However, contrary to the above-described conventional wisdom, Hofmann etal. have demonstrated that MG-based materials can be beneficiallyimplemented in a variety of other applications. For example, U.S. patentapplication Ser. No. 13/928,109 to Hofmann et al. describes how MG-basedmaterials can be developed for the fabrication of gears on a macroscale.In particular, U.S. patent application Ser. No. 13/928,109 explains thatwhile Ishida demonstrated the fabrication of MG-based gears, thedemonstration was limited inasmuch as the fabricated gears were ofsmaller dimensions (and thereby weren't subjected to the same modes offailure as macroscopic engineering component) and the gears operatedusing lubricant, which can mitigate tendencies for brittle fracture.(Id.) Generally, Hofmann et al. explain that the prior art has beenprincipally concerned with harnessing the wear resistance properties ofMG-based materials, and consequently focused on implementing the hardestMG-based materials. (Id.) This design methodology is limiting insofar asthe hardest materials are more prone to other modes of failure. (Id.)Indeed, Hofmann et al. demonstrate that implementing the hardestMG-based materials in the fabrication of macroscale gears generallyyields gears that fracture during operation. (Id.) Accordingly, Hofmannet al. disclose that MG-based materials can be developed to havefavorable properties with respect to fracture toughness, and thereby canbe made to fabricate macroscale gears that do not necessarily requirelubricant to function. (Id.) The disclosure of U.S. patent applicationSer. No. 13/928,109 is hereby incorporated by reference in its entirety,especially as it pertains to metallic glass-based materials, and theirimplementation in macroscale gears. Moreover, U.S. patent applicationSer. No. 13/942,932 to Hofmann et al. discloses that MG-based materialspossess other favorable materials properties that can also allow them tobe used in the fabrication of macroscale compliant mechanisms. Thedisclosure of U.S. patent application Ser. No. 13/942,932 is herebyincorporated by reference in its entirety, especially as it pertains tometallic glass-based materials, and their implementation in macroscalecompliant mechanisms.

The potential of metallic glass-based materials continues to beexplored, and developments continue to emerge. For example, in U.S.patent application Ser. No. 14/060,478, D. Hofmann et al. disclosetechniques for depositing layers of metallic glass-based materials toform objects. The disclosure of U.S. patent application Ser. No.14/060,478 is hereby incorporated by reference especially as it pertainsto metallic glass-based materials, and techniques for depositing them toform objects. Furthermore, in U.S. patent application Ser. No.14/163,936, D. Hofmann et al., disclose techniques for additivelymanufacturing objects so that they include metallic glass-basedmaterials. The disclosure of U.S. patent application Ser. No. 14/163,936is hereby incorporated by reference in its entirety, especially as itpertains to metallic glass-based materials, and additive manufacturingtechniques for manufacturing objects so that they include metallicglass-based materials. Additionally, in U.S. patent application Ser. No.14/177,608, D. Hofmann et al. disclose techniques for fabricating strainwave gears using metallic glass-based materials. The disclosure of U.S.patent application Ser. No. 14/177,608 is hereby incorporated byreference in its entirety, especially as it pertains to metallicglass-based materials, and their implementation in strain wave gears.Moreover, in U.S. patent application Ser. No. 14/178,098, D. Hofmann etal., disclose selectively developing equilibrium inclusions within anobject constituted from a metallic glass-based material. The disclosureof U.S. patent application Ser. No. 14/178,098 is hereby incorporated byreference, especially as it pertains to metallic glass-based materials,and the tailored development of equilibrium inclusions within them.Furthermore, in U.S. patent application Ser. No. 14/252,585, D. Hofmannet al. disclose techniques for shaping sheet materials that includemetallic glass-based materials. The disclosure of U.S. patentapplication Ser. No. 14/252,585 is hereby incorporated by reference inits entirety, especially as it pertains to metallic glass-basedmaterials and techniques for shaping sheet materials that includemetallic glass-based materials. Additionally, in U.S. patent applicationSer. No. 14/259,608, D. Hofmann et al. disclose techniques forfabricating structures including metallic glass-based materials usingultrasonic welding. The disclosure of U.S. patent application Ser. No.14/259,608 is hereby incorporated by reference in its entirety,especially as it pertains to metallic glass-based materials andtechniques for fabricating structures including metallic glass-basedmaterials using ultrasonic welding. Moreover, in U.S. patent applicationSer. No. 14/491,618, D. Hofmann et al. disclose techniques forfabricating structures including metallic glass-based materials usinglow pressure casting. The disclosure of U.S. patent application Ser. No.14/491,618 is hereby incorporated by reference in its entirety,especially as it pertains to metallic glass-based materials andtechniques for fabricating structures including metallic glass-basedmaterials using low pressure casting. Furthermore, in U.S. patentapplication Ser. No. 14/660,730, Hofmann et al. disclose metallicglass-based fiber metal laminates. The disclosure of U.S. patentapplication Ser. No. 14/660,730 is hereby incorporated by reference inits entirety, especially as it pertains to metallic glass-based fibermetal laminates. Additionally, in U.S. patent application Ser. No.14/971,848, Kennett et al. disclose fabricating gearbox housings frommetallic glass-based materials. The disclosure of U.S. patentapplication Ser. No. 14/971,848 is hereby incorporated by reference inits entirety, especially as it pertains to fabricating gearbox housingsfrom metallic glass-based materials and also as it pertains to castingmetallic glass-based materials around a solid body to form usefulobjects.

Notwithstanding all of these developments, the vast potential ofmetallic glass-based materials has yet to be fully appreciated. Theinstant application discloses how MG-based materials can be implementedin the creation of highly customized and/or robust strain wave gears andstrain wave gear components. Note that MG-based materials can bedeveloped so that they have high fatigue resistance, high fracturetoughness, excellent sliding friction properties, a low density, and ahigh elasticity. Moreover, these and other characteristics can belargely tunable, e.g. by alloying a given MG-based material or elseapplying some other processing (e.g. heat treating) to a MG-basedmaterial. This versatility can enable the implementation of highlycustomized and efficacious strain wave gears and/or strain wave gearingcomponents; e.g. they can be made to sustain greater operating loads, belighter, and/or have longer life cycles. Notably, the characteristicsthat MG-based materials can offer can give rise to unique designconsiderations that can enable the implementation of more robustconfigurations relative to those seen in conventional strain wave gears.The general operation of strain wave gears is now discussed in detailbelow.

Strain Wave Gear Operation

In many embodiments of the invention, strain wave gears and strain wavegear components are provided that incorporate MG-based materials andthereby have improved performance characteristics. To provide context,the basic operating principles of strain wave gears are now reviewed.

FIG. 1 illustrates an exploded view of a typical strain wave gear thatcan be fabricated from MG-based materials in accordance with embodimentsof the invention. In particular, the strain wave gear 100 includes awave generator 102, a flexspline 108, and a circular spline 112. Theillustrated wave generator 102 includes a wave generator plug 104 and aball bearing 106. Importantly, the wave generator plug 104 is ellipticalin shape, and is disposed within the ball bearing 106 so that the ballbearing 106 to conforms to the elliptical shape. In this arrangement,the outer race of the ball bearing 106 can rotate relative to the wavegenerator plug 104. In the illustrated embodiment, the flexspline 108 isdepicted as being in the shape of a cup; notably, the outer rim of thecup includes a set of gear teeth 110. In the illustration, theflexspline is fitted over the ball bearing, such that the outer rim ofthe flexspline conforms to the aforementioned elliptical shape. Notethat in this arrangement, the ball bearing allows the flexspline torotate relative to the wave generator plug. The circular spline, 112 isin the shape of a ring; importantly, the inner perimeter of the ringincludes a set of gear teeth. Normally, there are more gear teeth on thecircular spline 114 than on the flexspline 110. In many instances thereare two more gear teeth on the circular spline 112 than on theflexspline 108. Typically, the flexspline 108 is fitted within thecircular spline 112 such that the gear teeth of the flexspline 110engage the gear teeth of the circular spline 114. Notably, because thegear teeth of the flexspline 110 conform to an elliptical shape, onlythe gear teeth proximate the major axis of the elliptical shape engagethe gear teeth of the circular spline 114 in the usual case. Conversely,the gear teeth of the flex spline 110 that are proximate the minor axisof the elliptical shape are disengaged from the gear teeth of thecircular spline 114. In many instances, 30% of the gear teeth of theflexspline 110 are engaged with the gear teeth of the circular spline114. With this arrangement, the wave generator plug 104 can rotate in afirst direction about the central axis of the elliptical shape, andthereby cause the flexspline 108 to rotate in a second oppositedirection and at a different rate of rotation (generally slower) aboutthe central axis of the elliptical shape. This can be achieved as theflexspline 108 is made of a flexible material that can accommodate thedeflections that may result from the rotation of the wave generator plug104.

FIGS. 2A-2D depict the normal operation of a strain wave gear that canbe fabricated from MG-based materials in accordance with embodiments ofthe invention. In particular, FIG. 2A illustrates a strain wave gear,where the wave generator plug 204 is in a first orientation such thatthe major axis of the elliptical shape is vertical relative to thedrawing. This starting position is designated as ‘0° ’. An arrow 216designates one of the gear teeth of the flexspline 208 that isconsidered in FIGS. 2A-2D for purposes of illustration. FIG. 2Billustrates that the wave generator plug 204 has rotated clockwise 90°.The rotation of the wave generator plug 204 has caused the flexspline208 to deflect in a particular fashion; as a result, the gear toothcorresponding with the arrow 216 is disengaged from the gear teeth ofthe circular spline 214. Notably, the gear tooth corresponding with thearrow 216, has rotated slightly counterclockwise in association with the90° clockwise rotation of the wave generator plug 204. FIG. 2Cillustrates that the wave generator plug 204 has rotated clockwiseanother 90° so that it has now rotated 180° clockwise relative to theinitial starting position. In the illustration, gear tooth designated bythe arrow 216 has reengaged the gear teeth of the circular spline 214 ata position slightly counterclockwise relative to the initial startingposition. FIG. 2D illustrates that the wave generator plug 204 hasrotated a full 360° clockwise relative to the initial starting position.Consequently, the gear tooth indicated by 216 has rotated slightlyfurther counterclockwise than the position seen in FIG. 2C. In general,it is seen in FIGS. 2A-2D that a full 360° rotation of a wave generatorplug 204 in one direction results in a slight rotation of the flexspline208 in an opposite direction. In this way, strain wave gears can achieverelatively high reduction ratio within a small footprint. Typically aninput torque is applied to the wave generator plug 204, while theflexspline 208 provides a corresponding output torque.

Of course, it should be understood that while an example of a strainwave gear design is illustrated and discussed above, any suitable strainwave gear design and any suitable strain wave gear components can befabricated from MG-based materials in accordance with embodiments of theinvention. For example, the flexspline can take any suitable shape, andis not required to be ‘cup-shaped.’ Similarly, any type of bearing canbe implemented—not just a ball bearing. For example, needle rollerbearings may be implemented. To be clear, the instant application is notmeant to be limited to any particular strain wave gear design or strainwave gear component design. It is now discussed how MG-based materialscan be implemented within strain wave gear components to enhance theperformance of strain wave gears in accordance with embodiments of theinvention.

Metallic Glass-Based Strain Wave Gears and Strain Wave Gear Components

In many embodiments of the invention, MG-based materials areincorporated within strain wave gears and/or strain wave gearcomponents. In many instances, MG-based materials can be developed topossess desired materials properties that can make them very-well suitedfor the fabrication of the constituent components of a strain wave gear.For example, from the above-described strain wave gear operatingprinciples, it is evident that the ball bearing and the flexsplinedeflect in a periodic fashion with the rotation of the wave generatorplug. As a result, it would be desirable that those components befabricated from materials that have high fatigue strength. For example,FIGS. 3A and 3B depict how the fatigue strength of the flexspline is aprincipal determinant of the life of a strain wave gear. Notably, theflexspline in a strain wave gear typically fails when the flexsplinefatigues (as opposed to other modes of failure), which causes it topermanently deform. In particular, FIG. 3A illustrates variousrepresentative torque specifications relative to rated torque for steelstrain wave gears, and FIG. 3B illustrates the same information forMG-based strain wave gears. For FIGS. 3A-3B, the rated torque has beennormalized to 1 and the strain wave gears are assumed to have similargeometric configurations for purposes of comparison.

Generally, the fatigue limit of a material is defined by the number oftimes that the material can be stressed at a particular level before thematerial permanently deforms. Assuming the same cyclic load is appliedmany times, the lower the load, the longer the materials will lastbefore it deforms. The cyclic load at which a material can survive 10⁷cycles is generally referred to as the fatigue limit of the material. Ifthe material is cyclically loaded at its yield strength, it wouldpresumably fail in one cycle. Thus, fatigue limits are generallyreported as a percentage of their yield strength (to normalize theirperformance). As an illustration, a 300M steel has a fatigue limit whichis 20% of its yield strength. If one assumes a fixed geometry of a partbeing fatigued, as with a flexspline, incorporating a more flexiblematerial results in a lower stress per cycle, which can result in a muchlonger fatigue life.

Accordingly, MG-based materials can be favorably incorporated within aflexspline of a strain wave gear to provide enhanced fatigueperformance. For example, MG-based materials can have an elastic limitas high as 2%, and can also have a stiffness about 3 times lower thansteel-based materials. Typically, many MG-based materials candemonstrate elastic limits that are greater than approximately 1%, andit is these MG-based materials that can be particularly well-suited forimplementation within strain wave gear components. Many MG-basedmaterials can demonstrate elastic limits that are greater thanapproximately 1.5%. By contrast, 304 stainless steel has been reportedto have an elastic limit of 0.1%. Generally, this implies that aflexspline fabricated from a MG-based material can experience lowerstress per unit of deformation relative to a steel-based flexsplinehaving an identical geometry (e.g. as measured by a respectivematerial's yield strength). Correspondingly, the MG-based material canhave much more favorable fatigue properties, e.g. a material that issubjected to less relative stress tends to be capable of withstandingmore loading cycles. Importantly, whereas MG-based materials are oftenconsidered to be brittle and susceptible to fatigue failure by othermeasures, they can demonstrate great fatigue resistance when the appliedstresses that they are subjected to are relatively less.

Note also that the differing stiffness values impact the geometries ofthe fabricated components. Thus, because MG-based materials can haverelatively lower stiffness values (e.g. relative to steel), they canallow for strain wave gear components that have more favorablegeometries. For example, a relatively lower stiffness can enable theimplementation of a thicker flexspline, which can be advantageous.Indeed, the materials properties profile of MG-based materials generallycan enable the development of more favorable geometries—i.e. in additionto stiffness, the other materials properties of MG-based materials canalso contribute to the development of advantageous geometries.

Moreover, as is understood from the prior art, MG-based materials canhave higher hardness values, and correspondingly demonstrate improvedwear performance relative to heritage engineering materials. Materialswith high hardness values can be particularly advantageous in strainwave gears, as the constituent components of strain wave gears are incontinuous contact with one another and are subject to, for example,sliding friction. Generally, when gear teeth are subjected to a constantload and accompanying friction, the resulting associated elasticdeformation and wear can precipitate ‘ratcheting’. That MG-basedmaterials can have a high hardness value, good resistance to wear(including a good resistance to galling), and high elasticity—even whensubjected to high loads—can make them well-suited to be implementedwithin a strain wave gear. For example, the implementation of MG-basedmaterials within the gear teeth of a strain wave gear can deterratcheting. Furthermore, MG-based materials can be made to have a highhardness value throughout a broad temperature range. For example,MG-based materials can have a hardness value that does not vary as afunction of temperature by more than 20% within the temperature range of100K to 300K. Indeed, MG-based materials can have a strength that doesnot vary as a function of temperature by more than 20% within atemperature range of 100K to 300K. In general, the implementation ofMG-based materials within strain wave gears can be favorable on manylevels. Table 1 below illustrates how the materials properties ofcertain MG-based materials possess improved materials propertiesrelative to heritage engineering materials in many respects.

TABLE 1 Material Properties of MG-Based Materials relative to HeritageEngineering Materials Density Stiffness, E Tensile Yield Tensile UTSElastic Limit Specific Hardness Material (g/cc) (GPa) (MPa) (MPa) (%)Strength (HRC) SS 15500 H1024 7.8 200 1140 1170 <1 146 36 Ti—6Al—4V STA4.4 114 965 1035 <1 219 41 Ti—6Al—6V—4Sn STA 4.5 112 1035 1100 <1 230 42Nitronic 60 CW 7.6 179 1241 1379 <1 163 40 Vascomax C300 8.0 190 18971966 <1 237 50 Zr-BMG 6.1 97 1737 1737 >1.8 285 60 Ti-BMGMC 5.2 94 13621429 >1.4 262 51 Zr-BMGMC 5.8 75 1096 1210 >1.4 189 48

Importantly, materials properties of MG-based materials are a functionof the relative ratios of the constituent components and are also afunction of the crystalline structure. As a result, the materialsproperties of a MG-based material can be tailored by varying thecomposition and varying the ratio of crystalline structure to amorphousstructure. For example, in many embodiments it may be desirable toimplement MG-based materials having a particular materials profilewithin a particular component of a strain wave gear. In these instances,an appropriate MG-based material may be developed and/or selected fromwhich to fabricate a respective strain wave gear component. Tables 2, 3,and 4 depict how materials properties of MG-based materials can varybased on composition and crystalline structure.

TABLE 2 Material Properties of Select MG-Based Materials as a functionof Composition BMG bcc ρ σ_(y) σ_(max) ε_(y) E T_(s) name atomic %weight % (%) (%) (g/cm²) (g/cm³) (MPa) (%) (GPa) (K) DV2Ti₄₄Zr₂₀V₁₂Cu₅Be₁₉ Ti_(41.9)Zr_(36.3)V_(12.1)Cu_(6.3)Be_(3.4) 70 30 5.131597 1614 2.1 94.5 956 DV1 Ti₄₈Zr₂₀V₁₂Cu₅Be₁₅Ti_(44.3)Zr_(35.2)V_(11.8)Cu_(6.1)Be_(2.6) 53 47 5.15 1362 1429 2.3 94.2955 DV3 Ti₅₆Zr₁₈V₁₀Cu₄Be₁₂ Ti_(51.6)Zr_(31.6)V_(9.8)Cu_(4.9)Be_(2.1) 4654 5.08 1308 1309 2.2 84.0 951 DV4 Ti₆₂Zr₁₅V₁₀Cu₄Be₉Ti_(57.3)Zr_(26.4)V_(9.8)Cu_(4.9)Be_(1.6) 40 60 5.03 1086 1089 2.1 83.7940 DVAI1 Ti₆₀Zr₁₆V₉Cu₃Al₃Be₉Ti_(55.8)Zr_(28.4)V_(8.9)Cu_(3.7)Al_(1.6)Be_(1.6) 31 69 4.97 1166 11892.0 84.2 901 DVAI2 Ti₆₇Zr₁₁V₁₀Cu₅Al₂Be₅Ti_(62.4)Zr_(19.5)V_(9.9)Cu_(6.2)Al₁Be_(0.9) 20 80 4.97 990 1000 2.078.7 998 Ti-6-4a Ti_(86.1)Al_(10.3)V_(3.6) Ti₉₀Al₆V₄(Grade 5 Annealed)na na 4.43 754 882 1.0 113.8 1877 Ti-6-4s Ti_(86.1)Al_(10.3)V_(3.6)[Ref]Ti₉₀Al₆V₄(Grade 5 STA) na na 4.43 1100 1170 ~1 114.0 1877 CP-Ti Ti₁₀₀Ti₁₀₀ (Grade 2) na na 4.51 380 409 0.7 105.0 ~1930

TABLE 3 Material Properties of Select MG-Based Materials as a functionof Composition σ_(max) ε_(tot) σ_(y) ε_(y) E ρ G CIT RoA Alloy (MPa) (%)(MPa) (%) (GPa) (g/cm³) (GPa) (J) (%) νZr_(36.6)Ti_(31.4)Nb₇Cu_(5.9)Be_(19.1) (DH1) 1512 9.58 1474 1.98 84.35.6 30.7 26 44 0.371 Zr_(38.3)Ti_(32.9)Nb_(7.3)Cu_(6.2)Be_(15.3) (DH2)1411 10.8 1367 1.92 79.2 5.7 28.8 40 50 0.373Zr_(39.6)Ti_(33.9)Nb_(7.6)Cu_(6.4)Be_(12.6) (DH3) 1210 13.10 1096 1.6275.3 5.8 27.3 45 46 0.376 Zr_(41.2)Ti_(13.8)Cu_(12.5)Ni₁₀Be_(22.5)(Vitreloy 1) 1737 1.98 — — 97.2 6.1 35.9 8 0 0.355Zr_(56.2)Ti_(13.8)Nb_(5.0)Cu_(6.9)Ni_(5.6)Be_(12.5) (LM 2) 1302 5.491046 1.48 78.8 6.2 28.6 24 22 0.375

TABLE 4 Material Properties as a Function of Composition and Structure,where A is Amorphous, X, is Crystalline, and C is Composite A/X/C 2.0 HvE (GPa) (CuZr42Al7Be10)Nb3 A 626.5 108.5 (CuZr46Al5Y2)Nb3 A 407.4 76.9(CuZrAl7Be5)Nb3 A 544.4 97.8 (CuZrAl7Be7)Nb3 A 523.9 102.3Cu40Zr40Al10Be10 A 604.3 114.2 Cu41Zr40Al7Be7Co5 C 589.9 103.5Cu42Zr41Al7Be7Co3 A 532.4 101.3 Cu47,5Zr48Al4Co0.5 X 381.9 79.6Cu47Zr45Al5Y2 A 409.8 75.3 CuSOZrB0 X 325.9 81.3 CuZr41AlBe7Cr3 A 575.1106.5 CuZrAl5Be5Y2 A 511.1 88.5 CuZrAl5Ni3Be4 A 504.3 95.5 CuZrAl7 X510.5 101.4 CuZrAl7Ag7 C 496.1 90.6 CuZrAl7Ni5 X 570.0 99.2Ni40Zr28.5Ti16.5Be15 C 715.2 128.4 Ni40Zr8.5Ti16.5Cu5Al10 X 627.2 99.3Ni40Zr28.5Ti16.5Cu5Be10 C 668.2 112.0 Ni56Zr17Ti13Si2Sn3Be9 X 562.5141.1 Ni57Zr18Ti14Si2Sn3Be6 X 637.3 139.4Ti33.18Zr30.51Ni5.33Be22.88Cu8.1 A 486.1 96.9 Ti40Zr25Be30Cr5 A 465.497.5 Ti40Zr25Ni8Cu9Be18 A 544.4 101.1 Ti45Zr16Ni9Cu10Be20 A 523.1 104.2Vit 1 A 530.4 95.2 Vit105 (Zr52.5Ti5Cu17.9Ni14.6Al10) A 474.4 88.5 Vit106 A 439.7 83.3 Zr55Cu30Al10NiS A 520.8 87.2 Zr65Cu17.5Al7.5Ni10 A463.3 116.9 DH1 C 391.1 84.7 GHDT (Ti30Zr35Cu8.28Be26.8) A 461.8 90.5

FIG. 5 illustrates how the hardness of a titanium MG-based materialvaries in relation to the composition of the alloy. Generally, titaniumMG-based alloys tend to possess a number of characteristics that makethem particularly well-suited for the fabrication of strain wave gearsand strain wave gear components. For example, such alloys can haverelatively low densities, e.g. on the order of 4.5 g/cm³. By contrast,many steel-based materials have densities on the order of 8 g/cm³.Notably, crystalline Titanium based alloys may not be as suitable forimplementation within strain wave gears, as many crystalline Titaniumbased alloys are characterized by: poor wear resistance, low hardness,and/or difficult machinability. Accordingly, by using titanium in theform of a metallic glass-based material, titanium can be viablyimplemented into strain wave gears and strain wave gearing components.

Tables 5 and 6 below list reported data as to how fatiguecharacteristics with MG-based materials vary as a function ofcomposition.

TABLE 5 Fatigue Characteristics as a Function of Composition FractureFatigue Strength Geometry Loading Frequency R- limit Fatigue Material(MPa) (mm) mode (Hz) ratio (MPa) ratioZr_(56.2)Cu_(6.9)Ni_(5.6)Ti_(13.8)Nb_(5.0)Be_(12.5) 1480 3 × 3 × 30 4PB25 0.1 −296 0.200 CompositesZr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1900 3 × 3 × 50 4PB 250.1 −152 0.080 Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1900 2 ×2 × 60 3PB 10 0.1 768 0.404Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1900 2 × 2 × 60 3PB 100.1 359 0.189 Zr₄₄Ti₁₁Ni₁₀Cu₁₀Be₂₅ 1900 2.3 × 2.0 × 85 4PB 5-20 0.3 5500.289 Zr₄₄T₁₁Ni₁₀Cu₁₀Be₂₅ 1900 2.3 × 2.0 × 85 4PB 5-20 0.3 390 0.205Zr_(52.5)Cu_(17.9)Al₁₀Ni_(14.6)Ti₅ 1700 3.5 × 3.5 × 30 4PB 10 0.1 8500.500 (Zr₅₈Ni_(13.6)Cu₁₈Al_(10.4))₉₉Nb₁ 1700 2 × 2 × 25 4PB 10 0.1 5590.329 Zr₅₅Cu₃₀Ni₅Al₁₀ 1560 2 × 20 × 50 Plate 40 0.1 410 0.263 bend

TABLE 6 Fatigue Characteristics as a Function of Composition FractureFatigue Strength Geometry Loading Frequency R- limit Fatigue Material(MPa) (mm) mode (Hz) ratio (MPa) ratioZr_(56.2)Cu_(6.9)Ni_(5.6)Ti_(13.8)Nb_(5.0)Be_(12.5) 1480 Ø2.98 TT 10 0.1239 0.161 Composites Zr₅₅Cu₃₀Ni₅Al₁₀ Nano 1700 2 × 4 × 70 TT 10 0.1 −3400.200 Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1850 Ø2.98 TT 100.1 703 0.380 Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1850Ø2.98 TT 10 0.1 615 0.332Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1850 Ø2.98 TT 10 0.1567 0.306 Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1900 — CC 50.1 −1050 0.553 Zr_(41.2)Cu_(12.5)Ni₁₀Ti_(13.8)Nb_(5.0)Be_(22.5) 1900 —TC 5 −1 −150 0.079 Zr₅₀Cu₄₀Al₁₀ 1821 Ø2.98 TT 10 0.1 752 0.413Zr₅₀Cu₃₀Al₁₀Ni₁₀ 1900 Ø2.98 TT 10 0.1 865 0.455 Zr₅₀Cu₃₇Al₁₀Pd₃ 1899Ø2.98 TT 10 0.1 983 0.518 Zr₅₀Cu₃₇Al₁₀Pd₃ 1899 Ø5.33 TT 10 0.1 −9000.474 Zr_(52.5)Cu_(17.9)Al₁₀Ni_(14.6)Ti₅ 1660 6 × 3 × 1.5 TT 1 0.1 — —Zr_(52.5)Cu_(17.9)Al₁₀Ni_(14.6)Ti₅ 1700 Ø2.98 TT 10 0.1 907 0.534Zr₅₉Cu₂₀Al₁₀Ni₈Ti₃ 1580 6 × 3 × 1.5 TT 1 0.1 — — Zr₆₅Cu₁₅Al₁₀Ni₁₀ 1300 3× 4 × 16 TT 20 0.1 −280 0.215 Zr₆₅Cu₃₀Al₁₀Ni₅ 1560 1 × 2 × 5 TT 0.13 0.5— —

Although the data in tables 5 and 6 has been reported, one of theinventors of the instant application conducted independent fatiguetests, which to some extent contradict the reported values. FIGS. 4A and4B depict the results of the conducted tests.

In particular, FIG. 4A illustrates the fatigue resistance of MonolithicVitreloyl, Composite LM2, Composite DH3, 300-M Steel, 2090-T81 Aluminum,and Glass Ribbon. From these results, it is demonstrated that CompositeDH3 exhibits a high resistance to fatigue failure. For example,Composite DH3 shows that it can survive approximately 20,000,000 cyclesat a stress amplitude/tensile strength ratio of about 0.25. Note thatmonolithic Vitreloy 1 shows relatively poor resistance to fatiguefailure, which appears to contravene the results shown in Tables 5 and6. This discrepancy may be in part due to the rigor under which the datawas obtained. In particular, as the inventor of the instant applicationrealized that resistance to fatigue is a critical material property indetermining suitability for various applications, he obtained fatigueresistance data that was procured under the most stringent testingconditions. FIG. 4A is reproduced from Launey, PNAS, Vol. 106, No. 13,4986-4991, the disclosure of which is hereby incorporated by reference(and of which the one of the instant Inventors is a listed coauthor).

Similarly, FIG. 4B illustrates the fatigue resistance of DV1 (‘Agboat’—i.e., manufactured using semisolid processing), DV1(‘indus.’—manufactured using industry standard procedures), CompositeDH3, Composite LM2, Monolithic Vitreloyl, 300-M Steel, 2090-T81Aluminum, and Ti-6Al-4V bimodal. These results indicate that CompositeDV1 (Ag boat) exhibits even greater resistance to fatigue failure thanComposite DH3. Note that the results of the Composite DV1 testing variedgreatly based on how the Composite DV1 was manufactured. When it wasmanufactured using ‘Ag boat’ techniques (‘Ag boat’ refers to semisolidmanufacturing techniques, which are described in Hofmann, JOM, Vol. 61,No. 12, 11-17, the disclosure of which is hereby incorporated byreference.), it displayed far superior resistance to fatigue as comparedto when it was manufactured using industry standard techniques. Theinventors of the instant application believe that this discrepancy isdue to the fact that industry standard manufacturing processes do notprovide the type of rigor necessary to produce sufficiently purematerials, and this may be a function of the industry not recognizinghow critical material composition is in determining material properties,including resistance to fatigue failure. FIG. 4B was produced by Launeyin a collaboration that resulted in FIG. 4A, but FIG. 4B was notpublished in the above-cited article.

In general, FIGS. 4A and 4B indicate that MG-based materials can bedeveloped to have better fatigue characteristics than steel and otherheritage engineering materials. Importantly, FIGS. 4A and 4B depictrelative stress amplitude ratios, and as can be gleaned from table 1,MG-based materials can be made to possess greater ultimate tensilestrengths than many steels. Thus, MG-based materials can be made towithstand more loading cycles at higher stress levels than some steels.Moreover, as MG-based materials can be made to be less stiff, they canbe made to experience less stress per unit deflection, which can therebyresult in even greater fatigue performance.

From the above, it is clear that MG-based materials can possessadvantageous materials properties that can make them very well-suitedfor implementation within strain wave gear components. Any of the listedMG-based materials can be implemented within strain wave gear componentsin accordance with certain embodiments of the invention. More generally,MG-based materials can be tailored (e.g. via alloying and/or heattreating) to obtain a material having the desired materials profile forimplementation within a strain wave gear in accordance with embodimentsof the invention. Generally, a desired material property profile can bedetermined for a respective strain wave gear component, and a MG-basedmaterial conforming to the material property profile can be developedand implemented.

For example, in many embodiments where a less stiff material is desired,the relative ratios of B, Si, Al, Cr, Co, and/or Fe within a MG-basedcomposition is reduced. Similarly, in many embodiments where a lessstiff material is desired, the volume fraction of soft, ductiledendrites is increased; or alternatively, the amount of beta stabilizingelements, e.g. V, Nb, Ta, Mo, and/or Sn, are increased. Generally, inmetallic glass matrix composites, the stiffness of a material changes inaccordance with the rule of mixtures, e.g., where there are relativelymore dendrites, the stiffness decreases, and where there are relativelyless dendrites, the stiffness increases. Note that, generally speaking,when modifying the stiffness of MG-based materials, the stiffness ismodified largely without overly influencing other properties, e.g.elastic strain limit or the processability of the MG-based material. Theability to tune the stiffness independent of other material propertiesor influencing processability is greatly advantageous in designingstrain wave gears and strain wave gear components.

Moreover, just as the stiffness of MG-based materials can be tuned, theresistance to fatigue failure can also be tuned in accordance withembodiments of the invention. The alloying elements used to improveresistance to fatigue failure are largely experimentally determined.However, it has been observed that the same processing techniques thatare used to enhance fracture toughness also tend to beneficiallyinfluence resistance to fatigue failure. More generally, any of avariety of materials characteristics can be altered by appropriatelyalloying base materials. For instance, the hardness, toughness, fatiguelife, corrosion resistance, etc., can be modified by appropriatealloying. In many instances, these characteristics can be independentlytuned. This can enable great customizability for parts to be fabricated.

In any case, as should be clear from the above, any of the above-listedand described MG-based materials can be incorporated within strain wavegears and strain wave gear components in accordance with embodiments ofthe invention. More generally, any MG-based material can be implementedwithin strain wave gears and strain wave gear components in accordancewith embodiments of the invention. For example, in many embodiments theimplemented MG-based material is based in Fe, Zr, Ti, Ni, Hf, or Cu(i.e. those respective elements are present in the material in greateramounts than any other element). In some embodiments, a MG-basedmaterial that is implemented within a strain wave gear component is aCu—Zr—Al—X composition, where X can be one or more element, includingfor example: Y, Be, Ag, Co, Fe, Cr, C, Si, B, Mo, Ta, Ti, V, Nb, Ni, P,Zn, and Pd. In several embodiments, a MG-based material that isimplemented within a strain wave gear component is a Ni—Zr—Ti—Xcomposition, where X can be one or more element, including for exampleCo, Al, Cu, B, P, Si, Be, and Fe. In a number of embodiments, a MG-basedmaterial that is implemented within a strain wave gear component is aZr—Ti—Be—X composition, where X can be one or more element, includingfor example Y, Be, Ag, Co, Fe, Cr, C, Si, B, Mo, Ta, Ti, V, Nb, Ni, P,Zn, and Pd. In some embodiments, a strain wave gear component includes aMG-based material that is Ni₄₀Zr_(28.5)Ti_(16.5)Al₁₀Cu₅ (atomicpercent). In several embodiments a strain wave gear component includes aMG-based material that is (Cu₅₀Zr₅₀)_(x)Al₁₋₁₂Be₁₋₂₀Co_(0.5-5). In manyembodiments, a desired materials profile is determined for a givenstrain wave gear component, and a MG-based material that possess thedesired characteristics is used to construct the strain wave gearcomponent. As MG-based materials can possess many advantageous traits,their implementation within strain wave gear components can result inmuch more robust strain wave gears. The design methodology andfabrication of MG-based strain wave gears is now discussed in greaterdetail below.

Fabrication of Metallic Glass-Based Strain Wave Gears and Strain WaveGear Components

In many embodiments of the invention, strain wave gear components arefabricated from MG-based materials using casting or thermoplasticforming techniques. Using casting or thermoplastic forming techniquescan greatly enhance the efficiency by which strain wave gears and strainwave gear components are fabricated. For example, steel-based strainwave gear components are typically machined; because of the intricacy ofthe constituent components, the machining costs can be fairly expensive.By contrast, using casting or thermoplastic forming techniques in thedevelopment of strain wave gear components can circumvent excessivecostly machining processes.

A method of fabricating a strain wave gear component that incorporatescasting or thermoplastic forming techniques is illustrated in FIG. 6.The process includes determining 610 a desired materials profile for thecomponent to be fabricated. For example, where a flexspline is to befabricated, it may be desired that the constituent material have acertain stiffness, a certain resistance to fatigue failure, a certaindensity, a certain resistance to brittle failure, a certain resistanceto corrosion, a certain resistance to wear, a certain level ofglass-forming ability, etc. In many embodiments, material costs are alsoaccounted for (e.g. certain MG-based may be more or less expensive thanother MG-based materials). Generally, any parameters can be accountedfor in determining 610 the materials profile for the component to befabricated.

Note that any constituent component of a strain wave gear can befabricated in accordance with embodiments of the invention. As alludedto above, because the flexspline and the ball bearing are subject toperiodic deformation, it may be particularly advantageous that they beformed from a material having a high resistance to fatigue failure.Moreover, flexsplines and ball bearings may also benefit from beingformed from a material that possesses excellent resistance to wear,since those components experience constant contact and relative motionduring the normal operation of a strain wave gear (the gear teeth of theflexspline are subject to wear and the balls and inner and outer racesof the ball bearing may experience wear). In some embodiments the ballsof the ball bearing are fabricated from MG-based materials—in this way,the balls of the ball bearing can benefit from the enhanced wearresistance that MG-based materials can offer.

But it should be clear that any of the components of a strain wave gearcan be fabricated from MG-based materials in accordance with embodimentsof the invention. In some embodiments, the gear teeth of the circularspline are fabricated from MG-based materials. In this way, the gearteeth of the circular spline can benefit from the enhancedwear-performance characteristics that MG-based materials can offer. Insome embodiments, the gear teeth of the circular spline that arefabricated from a MG-based material are thereafter press-fit into adifferent, stiffer material—for example beryllium and titanium—to formthe circular spline, bearing in mind that it would be beneficial for thecircular spline to be relatively rigid to support the motion of theflexspline and the wave generator. In this way, MG-based materials areimplemented in the gear teeth of the circular spline where they canoffer enhanced wear performance, and a stiffer material can form theremainder of the circular spline where it can offer enhanced structuralsupport.

In many embodiments, the majority of the constituent components of astrain wave gear are fabricated from the same MG-based materials—in thisway, the respective strain wave gear can have a more uniform coefficientof thermal expansion. In any case, it should be clear that any of theconstituent components of a strain wave gear can be fabricated from aMG-based material in accordance with embodiments of the invention.

Returning to FIG. 6, a MG-based material is selected 620 that satisfiesthe determined materials profile. Any suitable MG-based material can beselected, including any of those listed above in Tables 1-5, anddepicted in FIGS. 4A-4B and 5. In many embodiments, MG-based materialsare particularly developed to satisfy the determined 610 materialsprofile, and are thereby selected 620. For example, in many embodiments,given MG-based materials are developed by alloying (e.g. as discussedabove) in any suitable way to tweak the materials properties. In anumber of embodiments, a MG-based material is developed by modifying theratio of crystalline structure to amorphous structure (e.g. as discussedabove) to tweak the materials properties. Of course, any suitable way ofdeveloping MG-based materials that satisfy the determined 610 materialsproperties may be implemented in accordance with embodiments of theinvention.

The selected 620 MG-based material is formed into the desired shape(e.g. the shape of the component to be fabricated), for examplethermoplastically or using a casting technique. While the fabrication ofgear-type components from MG-based materials via casting and/orthermoplastic techniques is not currently widespread, the inventors ofthe instant application have demonstrated the viability of suchtechniques for this purpose. For example, FIGS. 7A-7D schematicallyillustrate a gear having a 1 inch radius that had been fabricated from aMG-based material using a single casting step. In particular, FIG. 7Aillustrates the steel mold 702 that was used in the formation of thegear. FIG. 7B illustrates removal of the metallic glass matrix compositematerial 704 from the steel mold 702. FIG. 7C is a reproduction of anSEM image that was taken of the fabricated gear. FIG. 7D depicts an SEMimage demonstrating the fidelity of the fabricated component. Notably,the gear teeth were also implemented using this method of fabrication.In this way, the intricate and expensive machining of the gear teeth canbe avoided (by contrast, steel-based strain wave gear componentstypically rely on machining in the formation of the component). Thus, inaccordance with this teaching, in many embodiments, MG-based materialsare thermoplastically formed or cast into the shapes of the constituentcomponents of a strain wave gear. In many embodiments, MG-basedmaterials are thermoplastically formed or cast into the shapes of theconstituent components including the shapes of the gear teeth. Note alsothat any suitable thermoplastic forming or casting technique can beimplemented in accordance with embodiments of the invention. Forexample, the constituent components of a strain wave gear can be formedby one of: a direct casting technique, a forging technique, a spinforming technique, a blow molding technique, a centrifugal castingtechnique, a thermoplastic forming technique using MG-based powder, etc.As one of ordinary skill in the art would appreciate, the MG basedmaterial must be cooled sufficiently rapidly to maintain at least someamorphous structure. Of course it should be noted that strain wave gearcomponents can be formed from MG-based materials in any suitable manner,including by machining, in accordance with embodiments of the invention.

As an example, FIGS. 8A-8D illustrate a direct casting technique thatcan be implemented to form a constituent component of a strain wave gearin accordance with embodiments of the invention. In particular, FIG. 8Adepicts that a molten MG-based material 802 that has been heated to amolten state and is thereby ready to be inserted into a mold 804. Themold 804 helps define the shape of the component to be formed. FIG. 8Bdepicts that the molten MG-based material 802 is pressed into the mold804. FIG. 8C depicts that the mold 804 is released after the MG-basedmaterial has cooled. FIG. 8D depicts that any excess flash 806 isremoved. Thus, it is depicted that a strain wave gear component can befabricated using direct casting techniques in conjunction with aMG-based material in accordance with embodiments of the invention. Notethat it is generally not feasible to cast crystalline metals that aresuitable for implementation within strain wave gear components.

FIGS. 9A-9C illustrate another forming technique that can be implementedin accordance with embodiments of the invention. In particular, FIGS.9A-9C illustrate the thermoplastic forming of a MG-based material thatis in the form of a sheet in accordance with embodiments of theinvention. Specifically, FIG. 9A depicts that a sheet of MG-basedmaterial 902 that has been heated such that thermoplastic forming can beimplemented. In the illustrated embodiment, the sheet of MG-basedmaterial 902 is heated via a capacitive discharge technique, but itshould be understood that any suitable method of heating can beimplemented in accordance with embodiments of the invention. FIG. 9Bdepicts that a press is used to force the MG-based material into themold 904 to form the component to be fabricated. FIG. 9C depicts thatthe mold 904 is released and any excess flash 906 is removed. Thus, thedesired component is achieved.

As mentioned above, the heating of the MG-based material so that it iscapable of thermoplastic forming can be achieved in any suitable way inaccordance with embodiments of the invention. For example, FIGS. 10A-10Cdepict that the heating of MG-based material in the form of a sheet canbe accomplished by spinning friction. FIGS. 10A-10C are similar to thoseseen in FIGS. 9A-9C except that the MG-based sheet material is heatedfrictionally by the rotation of the press 1010 as it is pressed againstthe MG-based material 1002. In this way, the MG-based material can beheated to an extent that it can be thermoplastically formed. Thistechnique has been referred to as ‘spin forming.’

Note that although the above descriptions regard mechanically conformingMG-based material to mold, MG-based material can be formed into a moldin any suitable way in accordance with embodiments of the invention. Inmany embodiments, the MG-based material is made to conform to the moldusing one of: a forging technique, a vacuum-based technique, a squeezingtechnique, and a magnetic forming technique. Of course, the MG-basedmaterial can be made to conform to a mold in any suitable fashion inaccordance with embodiments of the invention.

FIGS. 11A-11C depict the forming a part using blow molding techniques.In particular, FIG. 11A depicts that a MG-based material is placedwithin a mold. FIG. 11B depicts that the MG-based material 1102 isexposed to pressurized gas or liquid that forces the MG-based materialto conform to the shape of the mold 1104. Typically, a pressurized inertgas is used. As before, the MG-based material 1102 is usually heated sothat it is sufficiently pliable and can be influenced by the pressurizedgas or liquid. Again, any suitable heating technique can be implementedin accordance with embodiments of the invention. FIG. 11C depicts thatdue to the force of the pressurized gas or liquid, the MG-based materialconforms to the shape of the mold 1104.

FIGS. 12A and 12B depict that centrifugal casting can be implemented toform the constituent component of the strain wave gear. In particular,FIG. 12A depicts that molten MG-based material 1202 is poured into amold 1204, and that the mold is rotated so that the molten MG-basedmaterial conforms to the shape of the mold.

FIGS. 13A-13C depict that MG-based material can be inserted into a moldin the form of powder, subsequently heated so that the material isthermoplastically formable, and thereby made to form the shape of thedesired constituent component in accordance with embodiments of theinvention. In particular, FIG. 13A depicts that MG-based material in theform of powder 1302 is deposited within a mold. FIG. 13B depicts thatthe MG-based material 1302 is heated and pressed so as to conform to theshape of the mold 1304. And FIG. 13C depicts that the MG-based materialhas solidified and thereby formed the desired component.

In general, it should be clear that any suitable technique forthermoplastically forming or casting the MG-based material can beimplemented in accordance with embodiments of the invention. Theabove-described examples are meant to be illustrative and notcomprehensive. Even more generally, any suitable technique for forming astrain wave gear component that constitutes a MG-based material can beimplemented in accordance with embodiments of the invention.

Referring back to FIG. 6, the process 600 further includes, if desired,performing 640 any post-forming operations to finish the fabricatedcomponent. For example, in some embodiments, the general shape of aflexspline is thermoplastically formed or cast, and gear teeth aresubsequently machined onto the flexspline. In some embodiments atwin-roll forming technique is implemented to install gear teeth onto aflexspline or a circular spline. FIG. 14 depicts a twin roll formingarrangement that can be used to implement gear teeth onto a flexspline.In particular, the arrangement 1400 includes a first roller thatsupports the motion of a flexspline 1402 through the arrangement, and asecond roller 1412 that acts to define the gear teeth onto theflexspline. The flex spline 1402 can be heated so that it is morepliable and ready to be defined by the second roller. Of course, theformed part can be finished using any suitable technique in accordancewith embodiments of the invention. For example, gear teeth can beimplemented using traditional machining techniques. Additionally, theformed part can be finished in any suitable way—not just to define gearteeth—in accordance with embodiments of the invention.

FIGS. 15A-15F illustrate the fabrication of a flexspline in accordancewith the process outlined in FIG. 6. In particular: FIG. 15A depicts amulti-piece mold that is used to cast the general shape of theflexspline; FIG. 15B depicts the assembled multi-piece mold that is usedto cast the general shape of the flexspline; FIG. 15C illustrates thecasting of the flexspline using MG-based material; FIG. 15D illustratesthe disassembling the mold; FIG. 15E illustrates the flexspline as ithas been removed from the mold; and FIG. 15F illustrates that aflexspline can be machined to include gear teeth after being cast from aMG-based material. Bear in mind that although the illustration depictsthat gear teeth are machined onto the flexspline, the flexspline couldhave been cast to include the desired gear teeth. In this way, costlymachining processes can be avoided.

Note that the formation techniques are extremely sensitive to processcontrol. In general, it is beneficial to have precise control over thefluid flow, venting, temperature, and cooling when forming the part. Forexample, FIG. 16 schematically illustrates several attempts at formingthe flexspline using a casting technique, and many of the attempts areclearly imperfect. In particular, the 7 samples to the left of the imagewere fabricated using a TiZrCuBe MG-based material having a density of5.3 g/cm³. The right-most sample in the image was fabricated fromVitreloy 1.

FIG. 17 illustrates that the above-described processes can be used tocreate parts of varying scale. As an example, FIG. 17 illustrates alarger flexspline fabricated in accordance with the above-describedprocesses, as well as a smaller flexspline fabricated in accordance withthe above-described processes. In this way, the above-describedprocesses are versatile.

It should be understood that although FIGS. 15-17 regard the fabricationof a flexspline, any strain wave gear component can be fabricated from aMG-based material in accordance with embodiments of the invention. Forexample, FIGS. 18A-18B illustrate a circular spline that has beenfabricated from a MG-based material. Specifically, FIG. 18A illustratesa titanium MG-based material that has been formed into a 1.5″ circularspline; FIG. 18B depicts the fabricated circular spline relative to afabricated flexspline. Although the circular spline is not depicted asincluding gear teeth, gear teeth can subsequently be machined into thecircular spline.

The above-described fabrication techniques can be used to efficientlyfabricate strain wave gears and strain wave gear components. Forexample, as alluded to above, expenses associated with machining thecomponents can be avoided using these techniques. Accordingly, the costfor fabricating a given strain wave gear component becomes principally afunction of the cost of the raw material, and this can be the caseirrespective of the size of the component. By contrast, when steel-basedstrain wave gear components are formed, the cost of manufacturing thepart may increase with a reduction in size beyond some critical value.This is because it becomes difficult to machine parts of a smaller size.

By way of example, FIG. 19 illustrates this relationship with respect toflexsplines where the cost of raw material for amorphous metal isgreater than that of steel. For example, the stiffness of steel mayrequire that flexsplines have a diameter less than some specifiedamount, e.g. 2 inches, and have a wall thickness of less than someamount, e.g. 1 mm. To provide context, FIG. 20 illustrates a steel-basedflexspline 2″ in diameter and having a wall thickness of 0.8 mm.Importantly, as flexsplines are made smaller, e.g. below 1 inch indiameter, the wall of the steel becomes too thin to machine easily. As aresult, even where the cost of the amorphous metal raw material isgreater than that of steel, the flexspline can be cheaper to manufacturefrom amorphous metal. In essence, burdensome machining could beeliminated by casting the part from a MG-based material, and the cost ofthe flexspline can thereby be reduced.

Customized Manufacturing Processes for the Fabrication of TailoredMetallic Glass-Based Materials

As can be appreciated from the above discussion, the implementation ofMG-based materials into strain wave gears and strain wave gearingcomponents can confer a host of advantages. For example, as alreadyalluded to above, the implementation of metallic glass-based materialscan result in the creation of more robust strain wave gears and strainwave gearing components. Moreover, as also alluded to above, metallicglass-based materials are amenable to casting and other thermoplasticmanufacturing strategies, which can be much more efficient manufacturingtechniques relative to conventional techniques typically employed inconstructing conventional steel-based strain wave gears (e.g.machining). In many embodiments of the invention, the informationdiscussed above is used to implement unique manufacturing strategies toproduce highly customized strain wave gears. For example, MG-basedmaterials can be made to possess unique materials property profiles, andthese materials profiles can influence design considerations.

For instance, in many embodiments, robust metallic glass-based strainwave gears having a relatively smaller dimension—e.g. having flexsplinescharacterized by a major diameter of less than approximately 4inches—are implemented using MG-based materials. In a number ofembodiments, robust metallic glass-based strain wave gears havingflexsplines characterized by a major diameter of less than approximately2 inches are implemented using MG-based materials. Conventionally, themanufacture of strain wave gears from steel at such small dimensions canbe challenging. In particular, in order for steel to be made to achievethe requisite level of flexibility for suitable flexspline operation atsuch small dimensions, it generally has to be made in the form of arelatively thin walled structure. However, because the flexspline has tobe made to conform to this thin shape, it can be undesirably fragile. Bycontrast, metallic glass-based materials can be relatively much thickerand still possess the requisite level of flexibility. This is becausemetallic glass-based materials can be made to be much less stiff thansteel-based materials. Accordingly, the thicker flexsplines made frommetallic glass-based materials can be much more durable. Moreover, itcan be much easier to cast thicker metallic glass-based as opposed tothinner metallic glass-based materials.

FIG. 21 illustrates a process for fabricating a strain wave gearflexspline characterized by a maximum diameter of less thanapproximately 4 inches in accordance with certain embodiments of theinvention. In particular, the process 2100 is similar to that describedwith respect to FIG. 6 insofar as it includes determining 2110 a desiredmaterials profile and selecting 2120 a suitable MG-based compositionfrom which the desired materials profile can be realized. Within thecontext of the instant application, the term “MG-based composition” canbe understood to reference an element or aggregation of elements thatare capable of forming a metallic glass-based material (e.g. via beingexposed to a sufficient cooling rate). As before, the selection 2120 canaccount for any of a variety of alloy variations—in other words, a basecomposition can be alloyed as desired in order to converge on a suitableMG-based composition that can yield the desired result. The materialsselection 2120 can also account for the application of any of a varietyof processing methodologies on a given composition. For instance, a basecomposition can be heat treated during the forming process so as todevelop desired crystalline phases within the context of a metallicglass composite. The method 2100 further includes forming 2130 theselected MG-based composition into the desired strain wave gearflexspline shape characterized by the desired materials properties, athickness of greater than approximately 1 mm and a major diameter ofless than approximately 4 inches. Of course, any suitable formingprocess can be implemented in accordance with embodiments of theinvention that can allow for the realization of the MG-based material,including casting processes and thermoplastic forming processes. Forinstance, casting processes can be implemented that allow forsufficiently rapid cooling rates (e.g. 1000 K/s) so as to cause theformation of an amorphous matrix can be implemented. In manyembodiments, the forming 2130 of the flexspline includes casting theselected MG-based material around a crystalline metal solid body. Thistechnique is disclosed in U.S. patent application Ser. No. 14/971,848(“the '848 app”), incorporated by reference above. This can be aneffective casting strategy as the formed MG-based material can be easilyremoved from the crystalline metal solid body since the crystallinemetal solid body will typically shrink upon the cooling of the castmaterial to a greater extent than the cast MG-based material (asdisclosed in the '848 app). In several embodiments, thermoplasticforming techniques are implemented to form the composition into thedesired shape. For example, any of the above-described thermoplasticforming techniques can be implemented. In a number of instances,localized thermoplastic forming processes are implemented. Localizedthermoplastic forming processes are disclosed in U.S. patent applicationSer. No. 14/252,585, and generally involve locally heating a metallicglass-based material within a first region to a temperature greater thanthe glass transition temperature of the metallic glass-based material,and deforming the metallic glass-based material within the first regionwhile the temperature of the metallic glass-based material within thefirst region is greater than its respective glass transitiontemperature. As can be appreciated, this can be achieved in any of avariety of ways. The disclosure of U.S. patent application Ser. No.14/252,585 is hereby incorporated by reference in its entirety,especially as it pertains to localized thermoplastic forming processes.More generally, any of a variety of forming processes can be implementedin accordance with embodiments of the invention.

Subsequent to forming processes, as before, any post-forming operationscan be performed 2140. In many instances, the formed 2130 flexsplinesare “net shape” and do not require any appreciable post-formingprocessing. In a number of embodiments, the formed 2130 flexsplines are‘near net shape’ and require minimal post-forming processing to finishthe part. For instance, surface finishes can be implemented. Anysuitable post-forming processing can be implemented in accordance withembodiments of the invention, including any of the processes mentionedpreviously with respect to FIG. 6.

FIGS. 22A-22C illustrate strain wave gear flexsplines having variousthicknesses for purposes of comparison. In particular, FIG. 22Aillustrates the wave generator and a flexspline of a conventionalsteel-based strain wave gear flexspline, characteristically possessing arelatively thin wall. FIG. 22B illustrates the wave generator and theflexspline of a strain wave gear manufactured from metallic glass-basedcomponents. In particular, it is depicted that the cup-shaped flexsplinehas a thicker wall than that of the steel-based flexspline seen in FIG.22A; however, the “toothed” portion of the flexspline is similar ingeometry to that seen in FIG. 22A. Correspondingly, the wave generatoralso maintains a similar geometry. In this way, the flexspline can berelatively more robust compared to the geometry illustrated in FIG. 22A,but can still accommodate a predefined wave generator geometry. FIG. 22Cillustrates that both the cup-portion of the flexspline and the toothedportion of the flexspline are made to be thicker from a MG-basedmaterial. In this instance, the wave generator would have to have adifferent geometry to accommodate the thicker toothed portion. TheMG-based material can be sufficiently flexible that suitable strain wavegear operation can be maintained even with the thicker geometry. Whereassmaller strain wave gears constructed from steel had to utilizethin-walled structures (generally less than 1 mm) in order to realizethe requisite flexibility, smaller strain wave gears constructed fromMG-based materials can be much thicker. In this way, strain wave gearsthat are more structurally resilient can be produced using MG-basedmaterials. Additionally, it can be much easier to cast metallicglass-based materials of greater thickness relative to casting thinwalled MG-based structures.

As an example, FIG. 23 depicts an isometric view of a thick-walledMG-based flexspline 2302 relative to an equivalent thin-walledsteel-based flexspline 2304.

While FIG. 21 illustrates a generalized process for fabricating aflexspline, it should be clear that the depicted process can be appliedand/or augmented in any of a variety of ways in accordance with manyembodiments of the invention. For example, in many embodiments, themethod further includes computing a maximum thickness that theflexspline can be made to possess and still viably operate under thedesired operating conditions based on the inherent structuralcharacteristics of the MG-based material to be implemented, and formingthe flexspline into the desired shape wherein the formed flexspline ischaracterized by a thickness of less than the computed thickness. Inmany instances the computed wall thickness accounts for the resistanceto fatigue failure. In many embodiments, the method is furthercharacterized insofar as the maximum thickness of the formed flexsplineis approximately 3 mm.

Notably, the ability to rely on casting and thermoplastic manufacturingtechniques can greatly enhance the customizability of the manufacture ofstrain wave gears. For example, strain wave gearing components can bemore readily cast in non-traditional shapes. Thus for example, in manyembodiments of the invention, flexsplines and/or circular splines arecast so that they include “S-shaped” teeth. Conventional gear teethgeometries can result in excessive and unwanted contact known asbacklash between intermeshing teeth. By contrast, gear teethcharacterized by S-shaped geometries can allow for minimized backlashand therefore smoother operation. FIGS. 24A and 24B illustrateconventional gear teeth geometries relative to S-shaped gear teethgeometry. In particular, FIG. 24A illustrates conventional gear teethgeometry, and highlights the area where backlash can be impactful. FIG.24B illustrates S-shaped gear teeth geometry that can be implemented viacasting and/or other thermoplastic forming techniques in accordance withmany embodiments of the invention. Of course, while the implantation ofS-shaped teeth is discussed and illustrated, any suitable componentshapes can be implemented in accordance with embodiments of theinvention. Casting and thermoplastic processes are versatile and lendthemselves the production of any of a variety of geometries.

While the above-discussion has regarded the implementation of MG-basedmaterials by utilizing them as the bulk material within respectivestrain wave gear components, in many embodiments, MG-based materials arecoated onto strain wave gears fabricated from more conventionalmaterials (e.g. steel and/or plastics). In this way, the wear-resistantproperties of any of a variety of MG-based materials can be harnessed.

As can be seen, the described manufacturing methods can enable theimplementation of highly customized strain wave gears. They can be madeto possess any of a variety of intrinsic materials properties based onthe implemented metallic glass-based materials. And they can alsoreadily be made to conform to unconventional, but advantageous,geometries. This level of customization is generally not feasible withconventional steel manufacturing methodologies.

As can be inferred from the above discussion, the above-mentionedconcepts can be implemented in a variety of arrangements in accordancewith embodiments of the invention. For example, in some embodiments,strain wave gear components are cast from polymeric materials, andsubsequently coated with bulk metallic glass-based materials. In thisway, the wear resistant properties of bulk metallic glass-basedmaterials can be harnessed. Accordingly, although the present inventionhas been described in certain specific aspects, many additionalmodifications and variations would be apparent to those skilled in theart. It is therefore to be understood that the present invention may bepracticed otherwise than specifically described. Thus, embodiments ofthe present invention should be considered in all respects asillustrative and not restrictive.

What claimed is:
 1. A method of fabricating a flexspline of a strainwave gear comprising: providing a mold having a shape of a flexspline;forming a MG-based composition into the flexspline using a formingtechnique comprising: heating an MG-based composition to a temperaturegreater than the glass transition temperature of the MG-basedcomposition, depositing the MG-based composition into the mold,conforming the MG-based composition to the shape of the mold while thetemperature of the MG-based composition within the first region isgreater than its respective glass transition temperature of the MG-basedcomposition, quenching the MG-based composition sufficiently rapidly tomaintain at least some amorphous structure in the MG-composition,removing the MG-based composition from the mold, and wherein the formingof the MG-based composition results in a formed flexspline comprising aMG-based material; and wherein the formed flexspline is characterizedby: at least a portion having a thickness of greater than approximately1 mm and a major diameter of less than approximately 4 inches.
 2. Themethod of claim 1, wherein the mold is an outer mold defining the finalshape of the flexspline, and wherein the MG-based composition is pouredinto and forcibly pressed against the mold.
 3. The method of claim 1,wherein the formed MG-based material has an entirely amorphousstructure.
 4. The method of claim 1, wherein the formed MG-basedmaterial is a metallic glass matrix composite.
 5. The method of claim 1,wherein the formed MG-based material is further characterized by theinclusion of at least one set of gear teeth.
 6. The method of claim 5,wherein the gear teeth have a non-linear tooth profile.
 7. The method ofclaim 1, wherein the MG-based composition is a MG-based compositioncomprising at least one material selected from the group of Cu, Ti andZr.
 8. The method of claim 1, wherein the selected MG-based compositionis a composite material that includes at least one of one of V, Nb, Ta,Mo, and Sn.
 9. The method of claim 1, wherein the formation of theflexspline is a net shape process.
 10. The method of claim 9, whereinthe flexspline comprises plurality of gear teeth formed to a near-netshape, and further comprising finishing the plurality of gear teeth toform the plurality of gear teeth into a net shape.
 11. The method ofclaim 1, wherein the formed flexspline has a wall characterized by amaximum thickness of less than approximately 3 mm.
 12. The method ofclaim 1, wherein the heating technique is one of: a capacitive dischargeforming technique and a frictional heating technique.
 13. The method ofclaim 1, wherein the conforming technique is one of: spin forming, blowmolding, and centrifugal casting.
 14. The method of claim 1, wherein theMG-composition is powderized and then fused during the heating.
 15. Themethod of claim 1, further comprising finishing the MG-material.
 16. Themethod of claim 1, wherein the flexspline comprises at least one grooveconfigured to contain at least one spherical body.
 17. The method ofclaim 1, wherein the MG-composition is initially provided as a feedstockformed as one or more sheets, wherein the sheet is at least partiallyamorphous and has sufficient volume to form the flexspline afterforming.
 18. The method of claim 17, wherein more than one sheet is usedto form the flexspline, and wherein the MG-composition forming eachsheet has insufficient glass forming ability to form a single sheet ofsufficient thickness to form the flexspline.
 19. The method of claim 18,wherein the more than one sheet collectively has sufficient thickness toform the flexspline.
 20. The method of claim 18, wherein the flexsplineis formed of a plurality of materials at least one of which is theMG-composition and at least one of which is a MG composite material.